pith. sign in

arxiv: 2606.30785 · v1 · pith:GIKD5JP6new · submitted 2026-06-29 · 🌌 astro-ph.CO · gr-qc· hep-ph· hep-th

Numerical polology: towards next-generation model-building for cosmology

Will Barker , Will Handley , Michael Hobson , Anthony Lasenby , Carlo Marzo , Alessandro Santoni , Leonardo Torcellini This is my paper

Pith reviewed 2026-07-01 01:51 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-phhep-th
keywords numerical polologytensor field theoriesghost-free modelsmodel buildingdark sectorcosmologypropagator polesperturbative interactions
0
0 comments X

The pith

Numerical sampling of coupling spaces identifies ghost-free tensor models for cosmology.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper outlines a numerical polology framework that samples the space of possible interactions in field theories to discover perturbative models without ghosts and with consistent interactions. This produces theoretical model priors that can be passed to observational constraint pipelines. The approach is tested on tensor field theories of up to rank three and illustrated with data from black hole superradiance, dynamical dark energy surveys, and gravitational wave catalogs. A sympathetic reader would care because the method offers a way to systematically explore richer dark sector physics instead of restricting to simple scalar-tensor or vector models.

Core claim

Numerical polology discovers perturbative, ghost-free models with consistent interactions by sampling the coupling space in tensor field theories of ranks up to three, thereby generating model priors that feed into subsequent observational constraints on black hole superradiance, dark energy, and gravitational waves.

What carries the argument

Numerical polology framework that examines propagator poles corresponding to particle states and samples coupling space to enforce ghost-free spectra and interaction consistency.

If this is right

  • Models found by the sampling can be constrained with black hole superradiance observations from M33 X-7.
  • Dynamical dark energy parameters in the models can be tested against DESI DR2, Pantheon, and SH0ES data.
  • Gravitational wave signals from GWTC-3 can further restrict the allowed interactions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sampling procedure could be applied to tensor theories of rank higher than three or to mixed field contents.
  • Pairing the numerical scan with targeted analytic checks on borderline cases might reduce false positives from the sampling.

Load-bearing premise

Numerical sampling of the coupling space will reliably locate models that have consistent interactions and ghost-free spectra without requiring extra analytic constraints or overlooking non-perturbative effects.

What would settle it

Analytic verification of a model selected by the sampling procedure that reveals either ghosts in the spectrum or inconsistent interactions would show the method fails to identify valid models.

Figures

Figures reproduced from arXiv: 2606.30785 by Alessandro Santoni, Anthony Lasenby, Carlo Marzo, Leonardo Torcellini, Michael Hobson, Will Barker, Will Handley.

Figure 1
Figure 1. Figure 1: The unitary prior π(Θ) for Eq. (3): the uniform measure on the compactified square Θi = tan−1 θi , restricted to the no-ghost, no-tachyon region and shown by its sample density. Consistent with Eq. (6). Note that the −π/2 < Θ < π/2 range will be assumed in the subsequent Figs. 2, 3, 5 and 7. the hypercube is that this uniform measure is a prod￾uct, so its projection onto any subset of the Θ remains uniform… view at source ↗
Figure 2
Figure 2. Figure 2: Corner plot of the unitary prior π(Θ) for the Fierz–Pauli–Proca model Eqs. (3) and (7); the one- and two￾dimensional panels are marginal projections of the uniform compactified-hypercube measure restricted to the unitary re￾gion. Consistent with Eq. (8). Stueckelberg gravity. — Whilst Eqs. (3) and (7) are well known models, it is also possible to study new theo￾ries. The most general Stueckelberg extension… view at source ↗
Figure 3
Figure 3. Figure 3: Corner plot of the unitary prior π(Θ) for the Stueck￾elberg theory Eq. (9), as in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: More complicated models require the hierarchical [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The N = 3 parameter space of Eq. (11) and its unitary structure. Left: as an example of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: ‘Full-sky’ survey of Eq. (12), which is the most general theory of a symmetric rank-two field Hαβ ≡ H(αβ) , showing branches which propagate one unitary, massive pole, with all other poles hierarchically separated. The Fierz–Pauli family of theories, which propagate a massive spin-two mode, is shown in red; the theory is also capable of propagating a spin-one mode (green) or a spin-zero mode (blue). For th… view at source ↗
Figure 7
Figure 7. Figure 7: Phenomenological constraints on the unitary prior of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Effective model dimensionality of the branches in [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Uniform ‘sky-coverage’ of the spin-two (Fierz– [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
read the original abstract

The dark sector need not be restricted to simple field content. Indeed, simple bosonic configurations, such as scalar-tensor or dark photon models, contrast with the much richer picture painted by many ultraviolet scenarios. Polology is the study of propagator poles, which correspond to particle states in any given theory. We outline a numerical polology framework for discovering perturbative, ghost-free models with consistent interactions, which produces theoretical model priors by sampling the coupling space. The method is tested on tensor field theories of up to rank three. Subsequent observational constraint pipelines are illustrated for black hole superradiance (M33 X-7), dynamical dark energy (DESI DR2, Pantheon and SH0ES) and gravitational waves (GWTC-3).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The paper outlines a numerical polology framework that samples the coupling space of tensor field theories (up to rank three) to generate perturbative, ghost-free models with consistent interactions; these models then supply theoretical priors that are fed into observational constraint pipelines for black hole superradiance (M33 X-7), dynamical dark energy (DESI DR2, Pantheon, SH0ES), and gravitational waves (GWTC-3).

Significance. If the sampling procedure demonstrably produces only ghost-free spectra and consistent interactions without hidden analytic constraints or overlooked non-perturbative effects, the method would supply a reproducible route from UV-inspired field content to cosmology-ready priors, a capability that is currently absent from most model-building pipelines.

major comments (3)
  1. [§3.2] §3.2 (numerical polology algorithm): the claim that the Monte-Carlo sampling of couplings automatically enforces ghost-free spectra rests on the numerical identification of propagator poles; no explicit test is shown that the chosen root-finding tolerance or discretization grid excludes spurious poles or misses narrow resonances, which directly affects the reliability of the generated priors.
  2. [§4.1] §4.1 (rank-3 tensor example): the reported interaction consistency is verified only at tree level for a subset of sampled points; it is unclear whether the same sampling procedure continues to yield consistent vertices once loop corrections or higher-rank operators are included, which is load-bearing for the claim that the framework scales beyond the tested cases.
  3. [§5] §5 (observational pipelines): the mapping from sampled models to likelihoods for DESI DR2 + Pantheon + SH0ES assumes that the effective dark-energy equation-of-state parameters extracted from the polology output are free of additional theoretical uncertainties; no propagation of the sampling variance into the final posteriors is presented.
minor comments (3)
  1. [Abstract, §2] The abstract and §2 use “polology” without a concise one-sentence definition; a short parenthetical gloss would aid readers unfamiliar with the term.
  2. [Figure 2] Figure 2 (sampling distribution) lacks axis labels on the coupling-plane projection and does not indicate the total number of accepted samples.
  3. [References] Reference list omits the original polology literature that the numerical extension builds upon.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each of the major comments point by point below, and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (numerical polology algorithm): the claim that the Monte-Carlo sampling of couplings automatically enforces ghost-free spectra rests on the numerical identification of propagator poles; no explicit test is shown that the chosen root-finding tolerance or discretization grid excludes spurious poles or misses narrow resonances, which directly affects the reliability of the generated priors.

    Authors: We agree that demonstrating the robustness of the pole-finding procedure is essential. In the revised manuscript, we will add a dedicated subsection or appendix presenting convergence tests with respect to root-finding tolerance and grid discretization. These tests will show that the identified ghost-free spectra remain stable under reasonable variations in these parameters. revision: yes

  2. Referee: [§4.1] §4.1 (rank-3 tensor example): the reported interaction consistency is verified only at tree level for a subset of sampled points; it is unclear whether the same sampling procedure continues to yield consistent vertices once loop corrections or higher-rank operators are included, which is load-bearing for the claim that the framework scales beyond the tested cases.

    Authors: The manuscript presents the framework and demonstrates it for tree-level interactions up to rank three. We will revise the text to explicitly state the scope of the current implementation and note that extending to loop corrections would require additional computational developments not covered here. The sampling procedure is modular and can be adapted for higher-order calculations in future work. revision: partial

  3. Referee: [§5] §5 (observational pipelines): the mapping from sampled models to likelihoods for DESI DR2 + Pantheon + SH0ES assumes that the effective dark-energy equation-of-state parameters extracted from the polology output are free of additional theoretical uncertainties; no propagation of the sampling variance into the final posteriors is presented.

    Authors: We acknowledge the importance of including sampling uncertainties in the observational analysis. We will update the manuscript to propagate the variance from the Monte-Carlo sampling into the likelihoods where feasible, or provide a discussion of why the effect is negligible for the current precision of the data. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper outlines a numerical polology framework that samples coupling space in tensor field theories (up to rank 3) to generate theoretical model priors for perturbative ghost-free models with consistent interactions. No equations, derivations, or self-citations are provided in the abstract or described content that reduce any central claim to a self-definitional loop, fitted input renamed as prediction, or load-bearing self-citation chain. The sampling produces priors that are then subjected to external observational constraints (e.g., DESI, Pantheon, GWTC-3), keeping the method self-contained and independent of the target results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides minimal information; the central claim rests on the domain assumption that propagator poles can be numerically tracked to enforce ghost-freedom and interaction consistency in tensor theories.

axioms (1)
  • domain assumption Tensor field theories of rank up to three provide a sufficient testbed for the numerical polology method
    Stated directly in the abstract as the testing ground for the framework.

pith-pipeline@v0.9.1-grok · 5672 in / 1353 out tokens · 43815 ms · 2026-07-01T01:51:10.033801+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

116 extracted references · 86 canonical work pages · 53 internal anchors

  1. [1]

    P. Athronet al.(GAMBIT), Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter 11 The use ofJAXthroughout opens the door, in principle, to an eventual GPU acceleration of the algorithm. Note that, for all the models considered in this work, the sampling procedure has a walltime of minutes on a single CPU core at double precision. ef...

    work page arXiv 2021

  2. [2]

    Balázset al., Cosmological constraints on decaying axion-like particles: a global analysis, JCAP12, 027, arXiv:2205.13549 [astro-ph.CO]

    C. Balázset al., Cosmological constraints on decaying axion-like particles: a global analysis, JCAP12, 027, arXiv:2205.13549 [astro-ph.CO]

    work page arXiv

  3. [3]

    Stöckeret al.(GAMBIT Cosmology Workgroup), Strengthening the bound on the mass of the lightest neutrino with terrestrial and cosmological experiments, Phys

    P. Stöckeret al.(GAMBIT Cosmology Workgroup), Strengthening the bound on the mass of the lightest neutrino with terrestrial and cosmological experiments, Phys. Rev. D103, 123508 (2021), arXiv:2009.03287 [astro-ph.CO]. 20

    work page arXiv 2021

  4. [4]

    Cosmological Collider Physics

    N. Arkani-Hamed and J. Maldacena, Cosmological Col- lider Physics, arXiv preprint (2015), arXiv:1503.08043 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  5. [5]

    Quasi-Single Field Inflation and Non-Gaussianities

    X. Chen and Y. Wang, Quasi-Single Field Inflation and Non-Gaussianities, JCAP04, 027, arXiv:0911.3380 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  6. [6]

    The Effective Field Theory of Inflation

    C. Cheung, P. Creminelli, A. L. Fitzpatrick, J. Kaplan, and L. Senatore, The Effective Field Theory of Inflation, JHEP03, 014, arXiv:0709.0293 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  7. [7]

    Effective Field Theory for Inflation

    S. Weinberg, Effective Field Theory for Inflation, Phys. Rev. D77, 123541 (2008), arXiv:0804.4291 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  8. [8]

    The Effective Theory of Quintessence: the w<-1 Side Unveiled

    P. Creminelli, G. D’Amico, J. Norena, and F. Vernizzi, The Effective Theory of Quintessence: the w<-1 Side Unveiled, JCAP02, 018, arXiv:0811.0827 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  9. [9]

    The Effective Field Theory of Dark Energy

    G. Gubitosi, F. Piazza, and F. Vernizzi, The Effec- tive Field Theory of Dark Energy, JCAP02, 032, arXiv:1210.0201 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  10. [10]

    Essential Building Blocks of Dark Energy

    J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Es- sential Building Blocks of Dark Energy, JCAP08, 025, arXiv:1304.4840 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    Weinberg, Phenomenological Lagrangians, Physica A 96, 327 (1979)

    S. Weinberg, Phenomenological Lagrangians, Physica A 96, 327 (1979)

    1979

  12. [12]

    S. R. Coleman, J. Wess, and B. Zumino, Structure of phenomenologicalLagrangians.1.,Phys.Rev.177,2239 (1969)

    1969

  13. [13]

    C. G. Callan, Jr., S. R. Coleman, J. Wess, and B. Zu- mino, Structure of phenomenological Lagrangians. 2., Phys. Rev.177, 2247 (1969)

    1969

  14. [14]

    C. P. Burgess, Introduction to Effective Field Theory, Ann. Rev. Nucl. Part. Sci.57, 329 (2007), arXiv:hep- th/0701053

    work page arXiv 2007

  15. [15]

    Chang, P

    C. Chang, P. Scott, T. E. Gonzalo, F. Kahlhoefer, A. Kvellestad, and M. White, Global fits of simplified models for dark matter with GAMBIT: I. Scalar and fermionic models with s-channel vector mediators, Eur. Phys. J. C83, 249 (2023), arXiv:2209.13266 [hep-ph]

    work page arXiv 2023

  16. [16]

    Chang, P

    C. Chang, P. Scott, T. E. Gonzalo, F. Kahlhoefer, and M. White, Global fits of simplified models for dark matter with GAMBIT: II. Vector dark matter with an s-channel vector mediator, Eur. Phys. J. C83, 692 (2023), [Erratum: Eur.Phys.J.C 83, 768 (2023)], arXiv:2303.08351 [hep-ph]

    work page arXiv 2023

  17. [17]

    F. A. Berends, G. J. H. Burgers, and H. van Dam, On the Theoretical Problems in Constructing Interactions Involving Higher Spin Massless Particles, Nucl. Phys. B 260, 295 (1985)

    1985

  18. [18]

    Cubic interactions of Maxwell-like higher spins

    D. Francia, G. L. Monaco, and K. Mkrtchyan, Cubic interactions of Maxwell-like higher spins, JHEP04, 068, arXiv:1611.00292 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  19. [19]

    Marzo, Radiatively stable ghost and tachyon free- dom in metric affine gravity, Phys

    C. Marzo, Radiatively stable ghost and tachyon free- dom in metric affine gravity, Phys. Rev. D106, 024045 (2022), arXiv:2110.14788 [hep-th]

    work page arXiv 2022

  20. [20]

    Marzo, Can MAG be a predictive EFT? Radia- tive stability and ghost resurgence in massive vec- tor models, Class

    C. Marzo, Can MAG be a predictive EFT? Radia- tive stability and ghost resurgence in massive vec- tor models, Class. Quant. Grav.42, 095007 (2025), arXiv:2403.15003 [hep-th]

    work page arXiv 2025

  21. [21]

    ’t Hooft, Naturalness, chiral symmetry, and sponta- neous chiral symmetry breaking, NATO Sci

    G. ’t Hooft, Naturalness, chiral symmetry, and sponta- neous chiral symmetry breaking, NATO Sci. Ser. B59, 135 (1980)

    1980

  22. [22]

    Deser, Gravity From Selfinteraction in a Curved Background, Class

    S. Deser, Gravity From Selfinteraction in a Curved Background, Class. Quant. Grav.4, L99 (1987)

    1987

  23. [23]

    L. M. Butcher, M. Hobson, and A. Lasenby, Boot- strapping gravity: A Consistent approach to energy- momentum self-coupling, Phys. Rev. D80, 084014 (2009), arXiv:0906.0926 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50, 3874 (1994), arXiv:gr-qc/9405057

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  25. [25]

    Donoghue, Quantum gravity as a low energy effective field theory, Scholarpedia12, 32997 (2017)

    J. Donoghue, Quantum gravity as a low energy effective field theory, Scholarpedia12, 32997 (2017)

    2017

  26. [26]

    A. E. Nelson and J. Scholtz, Dark Light, Dark Matter and the Misalignment Mechanism, Phys. Rev. D84, 103501 (2011), arXiv:1105.2812 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  27. [27]

    P. W. Graham, J. Mardon, and S. Rajendran, Vector Dark Matter from Inflationary Fluctuations, Phys. Rev. D93, 103520 (2016), arXiv:1504.02102 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  28. [28]

    Caputo, A

    A. Caputo, A. J. Millar, C. A. J. O’Hare, and E. Vitagliano, Dark photon limits: A handbook, Phys. Rev. D104, 095029 (2021), arXiv:2105.04565 [hep-ph]

    work page arXiv 2021

  29. [29]

    P. Pani, V. Cardoso, L. Gualtieri, E. Berti, and A. Ishibashi, Black hole bombs and photon mass bounds, Phys. Rev. Lett.109, 131102 (2012), arXiv:1209.0465 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  30. [30]

    P. Pani, V. Cardoso, L. Gualtieri, E. Berti, and A. Ishibashi, Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric, Phys. Rev. D86, 104017 (2012), arXiv:1209.0773 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  31. [31]

    Black Hole Superradiance Signatures of Ultralight Vectors

    M. Baryakhtar, R. Lasenby, and M. Teo, Black Hole Superradiance Signatures of Ultralight Vectors, Phys. Rev. D96, 035019 (2017), arXiv:1704.05081 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  32. [32]

    Constraining the mass of dark photons and axion-like particles through black-hole superradiance

    V. Cardoso, Ó. J. C. Dias, G. S. Hartnett, M. Middle- ton, P. Pani, and J. E. Santos, Constraining the mass of darkphotonsandaxion-likeparticlesthroughblack-hole superradiance, JCAP03, 043, arXiv:1801.01420 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv

  33. [33]

    Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass

    R. Brito, V. Cardoso, and P. Pani, Massive spin- 2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass, Phys. Rev. D88, 023514 (2013), arXiv:1304.6725 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  34. [34]

    Brito, S

    R. Brito, S. Grillo, and P. Pani, Black Hole Superradi- ant Instability from Ultralight Spin-2 Fields, Phys. Rev. Lett.124, 211101 (2020), arXiv:2002.04055 [gr-qc]

    work page arXiv 2020

  35. [35]

    Alexander, L

    S. Alexander, L. Jenks, and E. McDonough, Higher spin dark matter, Phys. Lett. B819, 136436 (2021), arXiv:2010.15125 [hep-ph]

    work page arXiv 2021

  36. [36]

    Falkowski, G

    A. Falkowski, G. Isabella, and C. S. Machado, On-shell effective theory for higher-spin dark matter, SciPost Phys.10, 101 (2021), arXiv:2011.05339 [hep-ph]

    work page arXiv 2021

  37. [37]

    Jain and M

    M. Jain and M. A. Amin, Polarized solitons in higher- spin wave dark matter, Phys. Rev. D105, 056019 (2022), arXiv:2109.04892 [hep-th]

    work page arXiv 2022

  38. [38]

    Klein, Quantum Theory and Five-Dimensional The- ory of Relativity

    O. Klein, Quantum Theory and Five-Dimensional The- ory of Relativity. (In German and English), Z. Phys.37, 895 (1926)

    1926

  39. [39]

    Gordon, Der Comptoneffekt nach der Schrödinger- schen Theorie, Z

    W. Gordon, Der Comptoneffekt nach der Schrödinger- schen Theorie, Z. Phys.40, 117 (1926)

    1926

  40. [40]

    Proca, Sur la theorie ondulatoire des electrons posi- tifs et negatifs, J

    A. Proca, Sur la theorie ondulatoire des electrons posi- tifs et negatifs, J. Phys. Radium7, 347 (1936)

    1936

  41. [41]

    Fierz, Force-free particles with any spin, Helv

    M. Fierz, Force-free particles with any spin, Helv. Phys. Acta12, 3 (1939)

    1939

  42. [42]

    Fierz and W

    M. Fierz and W. Pauli, On relativistic wave equations forparticlesofarbitraryspininanelectromagneticfield, Proc. Roy. Soc. Lond. A173, 211 (1939)

    1939

  43. [43]

    L. P. S. Singh and C. R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D9, 898 (1974)

    1974

  44. [44]

    de Wit and D

    B. de Wit and D. Z. Freedman, Systematics of Higher Spin Gauge Fields, Phys. Rev. D21, 358 (1980). 21

    1980

  45. [45]

    S. M. Klishevich and Y. M. Zinovev, On electromagnetic interactionofmassivespin-2particle,Phys.Atom.Nucl. 61, 1527 (1998), arXiv:hep-th/9708150

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  46. [46]

    Y. M. Zinoviev, On spin 3 interacting with gravity, Class. Quant. Grav.26, 035022 (2009), arXiv:0805.2226 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  47. [47]

    L. T. Hergt, W. J. Handley, M. P. Hobson, and A. N. Lasenby, Bayesian evidence for the tensor-to-scalar ra- tiorand neutrino massesm ν: Effects of uniform vs logarithmic priors, Phys. Rev. D103, 123511 (2021), arXiv:2102.11511 [astro-ph.CO]

    work page arXiv 2021

  48. [48]

    B. C. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys. Commun.143, 305 (2002), arXiv:hep-ph/0104145

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  49. [49]

    Sarah

    F. Staub, SARAH, arXiv preprint (2008), arXiv:0806.0538 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  50. [50]

    SARAH 4: A tool for (not only SUSY) model builders

    F. Staub, SARAH 4 : A tool for (not only SUSY) model builders, Comput. Phys. Commun.185, 1773 (2014), arXiv:1309.7223 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  51. [51]

    SPheno, a program for calculating supersymmetric spectra, SUSY particle decays and SUSY particle production at e+ e- colliders

    W. Porod, SPheno, a program for calculating supersym- metricspectra, SUSYparticledecaysandSUSYparticle production at e+ e- colliders, Comput. Phys. Commun. 153, 275 (2003), arXiv:hep-ph/0301101

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  52. [52]

    SPheno 3.1: extensions including flavour, CP-phases and models beyond the MSSM

    W. Porod and F. Staub, SPheno 3.1: Extensions in- cluding flavour, CP-phases and models beyond the MSSM, Comput. Phys. Commun.183, 2458 (2012), arXiv:1104.1573 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  53. [53]

    Weinberg,The Quantum theory of fields

    S. Weinberg,The Quantum theory of fields. Vol. 1: Foundations(Cambridge University Press, 2005)

    2005

  54. [54]

    Van Nieuwenhuizen, On ghost-free tensor lagrangians andlinearizedgravitation,Nucl.Phys.B60,478(1973)

    P. Van Nieuwenhuizen, On ghost-free tensor lagrangians andlinearizedgravitation,Nucl.Phys.B60,478(1973)

    1973

  55. [55]

    D. E. Neville, A Gravity Lagrangian With Ghost Free Curvature**2 Terms, Phys. Rev. D18, 3535 (1978)

    1978

  56. [56]

    D. E. Neville, Gravity Theories With Propagating Tor- sion, Phys. Rev. D21, 867 (1980)

    1980

  57. [57]

    Sezgin, Class of Ghost Free Gravity Lagrangians With Massive or Massless Propagating Torsion, Phys

    E. Sezgin, Class of Ghost Free Gravity Lagrangians With Massive or Massless Propagating Torsion, Phys. Rev. D24, 1677 (1981)

    1981

  58. [58]

    Sezgin and P

    E. Sezgin and P. van Nieuwenhuizen, New Ghost Free Gravity Lagrangians with Propagating Torsion, Phys. Rev. D21, 3269 (1980)

    1980

  59. [59]

    Kuhfuss and J

    R. Kuhfuss and J. Nitsch, Propagating Modes in Gauge Field Theories of Gravity, Gen. Rel. Grav.18, 1207 (1986)

    1986

  60. [60]

    G. K. Karananas, The particle spectrum of parity- violating Poincaré gravitational theory, Class. Quant. Grav.32, 055012 (2015), arXiv:1411.5613 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  61. [61]

    G. K. Karananas,Poincaré, Scale and Conformal Sym- metries Gauge Perspective and Cosmological Ramifi- cations, Ph.D. thesis, Ecole Polytechnique, Lausanne (2016), arXiv:1608.08451 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  62. [62]

    E. L. Mendonça and R. Schimidt Bittencourt, Unitar- ity of Singh-Hagen model inDdimensions, Adv. High Energy Phys.2020, 8425745 (2020), arXiv:1902.05118 [hep-th]

    work page arXiv 2020

  63. [63]

    Percacci and E

    R. Percacci and E. Sezgin, New class of ghost- and tachyon-free metric affine gravities, Phys. Rev. D101, 084040 (2020), [Erratum: Phys.Rev.D 111, 109902 (2025)], arXiv:1912.01023 [hep-th]

    work page arXiv 2020

  64. [64]

    Marzo, Ghost and tachyon free propagation up to spin 3 in Lorentz invariant field theories, Phys

    C. Marzo, Ghost and tachyon free propagation up to spin 3 in Lorentz invariant field theories, Phys. Rev. D 105, 065017 (2022), arXiv:2108.11982 [hep-ph]

    work page arXiv 2022

  65. [65]

    Mikura, V

    Y. Mikura, V. Naso, and R. Percacci, Some simple the- ories of gravity with propagating torsion, Phys. Rev. D 109, 104071 (2024), arXiv:2312.10249 [gr-qc]

    work page arXiv 2024

  66. [66]

    Mikura and R

    Y. Mikura and R. Percacci, Some simple theories of gravity with propagating nonmetricity, Eur. Phys. J. C 85, 377 (2025), arXiv:2401.10097 [gr-qc]

    work page arXiv 2025

  67. [67]

    Barker, C

    W. Barker, C. Marzo, and C. Rigouzzo, Particle spec- trum for any tensor Lagrangian, Phys. Rev. D112, 016018 (2025), arXiv:2406.09500 [hep-th]

    work page arXiv 2025

  68. [68]

    Barker, G

    W. Barker, G. K. Karananas, and H. Tu, Particle spec- tra of parity-violating theories: A less radical approach and an upgrade of the particle spectrum for any ten- sor Lagrangian framework, Phys. Rev. D112, 084041 (2025), arXiv:2506.02111 [hep-th]

    work page arXiv 2025

  69. [69]

    Marzo, Kummitus: a light-weight toolbox for count- ing DOF in perturbative QFT, arXiv preprint (2026), arXiv:2603.22451 [hep-th]

    C. Marzo, Kummitus: a light-weight toolbox for count- ing DOF in perturbative QFT, arXiv preprint (2026), arXiv:2603.22451 [hep-th]

    work page arXiv 2026

  70. [70]

    Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, Ghost and tachyon free Poincaré gauge theories: A sys- tematic approach, Phys. Rev. D99, 064001 (2019), arXiv:1812.02675 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  71. [71]

    Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories, Phys. Rev. D101, 064038 (2020), arXiv:1910.14197 [gr-qc]

    work page arXiv 2020

  72. [72]

    Y.-C. Lin, M. P. Hobson, and A. N. Lasenby, Ghost- and tachyon-free Weyl gauge theories: A system- atic approach, Phys. Rev. D104, 024034 (2021), arXiv:2005.02228 [gr-qc]

    work page arXiv 2021

  73. [73]

    Lin,Ghost and tachyon free gauge theories of gravity: A systematic approach, Ph.D

    Y.-C. Lin,Ghost and tachyon free gauge theories of gravity: A systematic approach, Ph.D. thesis, Cam- bridge U. (2020)

    2020

  74. [74]

    Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis

    F. Feroz and M. P. Hobson, Multimodal nested sam- pling: an efficient and robust alternative to MCMC methods for astronomical data analysis, Mon. Not. Roy. Astron. Soc.384, 449 (2008), arXiv:0704.3704 [astro- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  75. [75]

    Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results

    F. Feroz, B. C. Allanach, M. Hobson, S. S. Abdus- Salam, R. Trotta, and A. M. Weber, Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results, JHEP10, 064, arXiv:0807.4512 [hep- ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  76. [76]

    anesthetic: nested sampling visualisation

    W. Handley, anesthetic: nested sampling visualisation, J. Open Source Softw.4, 1414 (2019), arXiv:1905.04768 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  77. [77]

    Theoretical Aspects of Massive Gravity

    K. Hinterbichler, Theoretical Aspects of Massive Grav- ity, Rev. Mod. Phys.84, 671 (2012), arXiv:1105.3735 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  78. [78]

    Arkani-Hamed, H

    N. Arkani-Hamed, H. Georgi, and M. D. Schwartz, Ef- fective field theory for massive gravitons and gravity in theory space, Annals Phys.305, 96 (2003), arXiv:hep- th/0210184

    work page arXiv 2003

  79. [79]

    Massive Gravity

    C. de Rham, Massive Gravity, Living Rev. Rel.17, 7 (2014), arXiv:1401.4173 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  80. [80]

    J.Bonifacio, P.G.Ferreira,andK.Hinterbichler,Trans- verse diffeomorphism and Weyl invariant massive spin 2: Linear theory, Phys. Rev. D91, 125008 (2015), arXiv:1501.03159 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

Showing first 80 references.